One Chapter 2

Work - Force and Displacement

• The work done on an object is dependant upon the force applied and the distance the force is applied over.

• F is the applied force, Dd is the displacement over which the force is applied, and w is the work done.
• Remember that there are two types of vector multiplication
  • Dot Product (Like work)

• C is a scalar quantity, A and B are the vectors being multiplied, |A| and |B| are the magnitudes of the two vectors and q is the smallest angle between vectors A and B.
• Cross Product

• Notice that A X B is not in the same direction as B X A, therefore cross products are not commutative.
• Work is a dot product (i.e. work is a scalar)
  • It is only the component of the force parallel to the displacement that does the work.
• The unit of work is the N.m which is given the name Joule (J).

1 J = 1 N.m = 1 kgm²/s²

• Joule - the work done by an applied force of 1 N acting through a displacement of 1 m in the same direction as the displacement.

Work - Area Under the F - d Graph

• The equation for work (w = F.d) is used if the force is kept constant.
• Force does not always remain constant.
• If force is not constant then work done = the Area under the Fcos(q) versus d graph.
• It is possible to have a negative work
  • if displacement moved is in the opposite direction to the applied force
  • work is done on the source of the force
  • graphically, this is area below the displacement axis.

Summary

1. Work is done on an object by an applied force, if there is a component of the force in the direction of the motion.
2. Force is in Newtons, Dd is in meters and work is in Joules in the work formula below

1. If the applied force varies in magnitude or direction, then the work is the area between the displacement axis and the line.
2. Area below the displacement axis is negative work, and above the displacement axis is positive work.

Kinetic Energy

• Consider a constant force applied to an object on a straight horizontal frictionless surface. F = the applied Force, Dt = the time the force is applied for, Dd = displacement over which the force is applied, and V₁ and V₂ are initial and final velocities respectively.

• Kinetic Energy - Energy of motion as defined by the equation above.
  • The units of kinetic energy is the Joule

1 J = 1 N.m = 1 kgm²/s²

• This is the same unit that we have used for work.

Kinetic Energy and Momentum

Potential Energy and the Law of Conservation of Energy

• An object which has kinetic energy can do work on an object.
  • a moving van crashes through a fence. It applies a force through a distance to the fence therefore it does work.
  • The change in kinetic energy = the work done in these cases
  • Therefore kinetic energy can do work or work can change the kinetic energy
• Energy - the ability to do work
  • Energy and work are really the same thing
• There are other types of energy besides kinetic energy.
  • A rock at the top of a hill has the ability to do work, because it could role down the hill and strike something.
  • A compressed or stretched spring has the ability to do work.
  • Magnets have an ability to do work by attracting other magnets.
• Potential Energy - Energy due to position or condition.
• Since work and energy are the same thing, we can calculate potential energy (E_p) by calculating the work done to put a system into its position or condition.
• The calculation of Potential energy requires the choosing of a reference point.

• The potential energy of the rock at the top of a cliff depends upon whether the ledge or the base of the cliff is the reference point. Obviously, if the rock falls to the ledge, it cannot do as much work as it could if it fell to the base of the cliff.
• Consider this situation.

• If the rock was at the base of the cliff, then to put the rock at the top, we would have to apply a force (-mg) over a displacement equal to the height of the cliff. Therefore,

• The relationship between work and energy leads to the law of conservation of energy.
• Law of Conservation of Energy - Energy is not created or destroyed in any interaction but is merely transformed from one type of energy to the next without loss.
• Transformation from one type of energy to another occurs when one part of a system does work on another part of the system.
  • A rock falls off of a cliff. Gravity does work on the rock to cause it to fall. This transforms potential energy to kinetic energy.
  • A stretched slingshot is released to shoot a rock. The slingshot has potential energy which is used to do work on the rock to give it kinetic energy.
  • A magnetic latch pulls a refrigerator door shut.

December 6, 2013